Question

For the demand curve P = 100 – 0.5Q, find the elasticity at P = 40. Instructions: Round your answer to 2 decimal places. If you are entering a negative number, be sure to include a negative sign (-).

Answer 1

The price elasticity of demand at P = 40 for the demand curve P = 100 - 0.5Q is -0.67. This is determined by substituting the price into the demand equation to find Q and then using the elasticity formula.

Step-by-step explanation:

The main answer to the question at hand involves calculating the price elasticity of demand. Given the demand curve P = 100 – 0.5Q, we need to find the elasticity at P = 40. The elasticity of demand measures the responsiveness of the quantity demanded when the price changes.To find the quantity demanded Q at P = 40, we substitute 40 into the demand equation: 40 = 100 - 0.5Q, which simplifies to Q = 120. To find elasticity, we use the formula:
Elasticity = (P/Q) * (dQ/dP). From the demand equation dQ/dP = -2 since the slope of the demand curve is the negative reciprocal of 0.5. Thus, Elasticity = (40 / 120) * (-2) = -2/3, which rounds to -0.67.Price elasticities of demand are typically negative due to the law of demand, with the absolute value indicating how responsive the demand is to price changes.